Can Undamped Natural Frequencies Be Complex Numbers?

[Frenchouille]

Hello everybody,

I have a question about the undamped natural frequencies for a three degree of freedom system.

The equation of motion for the undamped system is :

M$$\ddot{x}$$+K$$\dot{x}$$=0

The undamped natural frequencies I found is a complex number : $$\omega$$²=-187.29

Is this kind of result is possible? I'm surprised by the result I found since every time I've done a similar exercise before, the frequencies were always real numbers.

Thanks for your advices!

 

[mark726]

Hello,

Thank you for your question. The result you found for the undamped natural frequencies of a three degree of freedom system is indeed possible. In fact, it is not uncommon for the natural frequencies of a system to be complex numbers. This can happen when the system has multiple modes of vibration, each with a different natural frequency.

In your equation of motion, the terms M and K represent the mass and stiffness matrices, respectively. When you solve for the natural frequencies, you are essentially finding the eigenvalues of these matrices. In a three degree of freedom system, there are three eigenvalues, each corresponding to a different mode of vibration.

In some cases, these eigenvalues may be complex numbers, which means that the corresponding natural frequencies will also be complex. This can happen when the system has a combination of damping and stiffness, or when there are multiple modes of vibration that interact with each other.

So, to answer your question, yes, it is possible for the undamped natural frequencies of a three degree of freedom system to be complex numbers. I would suggest further examining your system and its parameters to understand why this result occurred. I hope this helps and good luck with your research!